The reflexive and anti-reflexive solutions of the matrix equation AHXB=C

Authors:
Xiang-yang Peng;Xi-yan Hu;Lei Zhang
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China and Department of Information and Computing Science, ChangSha University, Changsha 410003, PR China;College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China;College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 1
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Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1+A2X2B2=C

Mathematical and Computer Modelling: An International Journal

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Abstract

In this paper, the necessary and sufficient conditions for the solvability of matrix equation A^HXB=C over the reflexive or anti-reflexive matrices are given, and the general expression of the solution for a solvable case is obtained. Moreover, the relative optimal approximation problem is considered. The explicit expressions of the optimal approximation solution and the minimum norm solution are both provided.